The advantage of Case sensitivity is that you can have 131,072 different copies of thattennisgirl.jpg all called the same thing, whilst also being separate entities, or, more general, options, where n is the number of alphabetical letters in the text. This can also be seen as a logic error of such scale that it would accelerate the end of the universe.

Case sensitivity makes finding your pr0n a lot harder than it needs to be.
Rather than having to remember if you're trying to find mysister.jpg, yoursister.jpg, bobssister.jpg or oprah.jpg, you also have to choose between MySister.jpg, mysister.jpg, MYSISTER.JPG, yoursister.jpg, YourSister.jpg and YoursIsTER.jpg.

Another obvious advantage of CaSe iNSeNSiTiViTy is the possibility to type faster, as the Magic Keys (Shift and CAPS LOCK) on your keyboard are to be pressed by the shortest and least developed of your fingers (The ones anatomically attached your hand, you sex-focused pervert...). This agony is even worsened by the convention to press that shift button which is further away from the actual letter. Lower-case typing is widely common among users of Instant Messaging and Online Chat (see below for more information).

Approximately 1 in 30 human beings is Case sensitive. In particularly bad cases, BOLD CAPITALS or inconsistent use of capitalisation (eg. iPod) can cause Case-Induced fits not dissimilar to epilepsy or biscuits. If you see somebody suffering from a Case-Induced fits, try to talk them out of it by speaking either very very quietly, or VERY VERY LOUDLY INDEED.

God. Never ever forget His Case sensitivity. Otherwise, be prepared for His Holy Wrath.

Teachers. Although they are far from being as mighty as God, they can still force you to a lap of honour at school.

HaXX0Rz. Being Case sensitive is a crucial part of 1337|\|355, or at least they think so.

A common case insensitive keyboard.

UNIX-based systems, such as Linux. This is quite evident, as most users of such systems are HaXX0Rz.

Germans. The Germans, having a very idiosyncratic Grammar, pride themselves of being Case sensitive. They do not care about the People committing Suicide upon unsuccessfully having tried to master the german Language.

Article titles on Wikipedia (except for the first character after the colon!).

It MaKeS fInDiNg FiLeS, fOlDeRs AnD oThEr SuCh ItEmS iNfInItElY mOrE dIfFiCuLt, As YoU hAvE tO wOrRy AbOuT nAmEs LiKe MySister.jpg, mysister.jpg, MYSISTER.JPG As OpPoSeD tO mErElY rEmEmBeRiNg If It Is MySister.jpg Or YourSister.jpg.

iT iS WiDeLY CoMMoN aMoNG WaNNaBe-HaXX0RZ To SPeLL VoWeLS iN LoWeRCaSe, aND CoNSoNaNTS iN UPPeRCaSe, HoWeVeR, THiS RuLe iS NoT STRiCTLy FoLLoWeD FoR SCHiZoPHReNiCS SuCH aS THe LeTTeR Y. aPaRT FRoM THe HiGH LiaBiLiTY To eRRoRs and THe NeaR-uNReaDaBiLiTy, THeSe PeoPLe TYPe uNBeLieVaBLY SLoW aND THeReFoRe aRe FaR aWaY FRoM BeiNG a HaXX0R.

fURTHERMORE, IT IS A VERY COMMON BEGINNER'S MISTAKE TO FORGET TO TURN OFF cAPS lOCK AFTER yelling. tHIS OVERSIGHT OFTEN CAUSES MISUNDERSTANDINGS, AS OTHERS BELIEVE THE CONCERNED PERSON IS SHOUTING. sUCH INCIDENCES ARE FREQUENT CAUSES FOR KICKS FROM irc CHANNELS.